Tropical Storm Beryl made landfall early on Monday in north-east Florida, bringing drenching rains and driving winds to the southeastern US coast on the country's Memorial Day holiday, forecasters said.

The storm hit Florida around 12:10am with near-hurricane-strength winds of 70mph (113kph), according to the US national hurricane centre. It was expected to continue dumping rain over Florida and Georgia on Monday, before weakening as it moves inland and then heads out into the Atlantic Ocean.

A tropical storm warning remained in effect early on Monday for coastal areas of Florida and South Carolina, causing shoreline campers to pack up and head inland, with delays expected to holiday traffic.

The Florida governor, Rick Scott, urged residents in the affected areas to "stay alert and aware".

"Tropical Storm Beryl is expected to bring heavy rain and winds, and it is vital to continue to monitor local news reports and listen to the advice of local emergency management officials," Scott said in a statement on Sunday evening.

Campers at Cumberland Island, Georgia, which is accessible only by boat, were told to leave by 4:45 pm on Sunday. The island has a number of undeveloped beaches and forests popular with campers.

At Greyfield Inn, a 19th-century mansion and the only private inn on Cumberland Island, the rooms were almost all booked on Sunday and everyone was planning to stay put through the wet weather, said Dawn Drake, who answered the phone at the inn's office on the Florida coast.

In Jacksonville, Florida, Sunday's jazz festival and Memorial Day ceremony were cancelled. Workers were also out clearing tree limbs and debris. Winds had already knocked down trees and power lines in parts of coastal Georgia, leaving hundreds without electricity.

But business was booming at the Red Dog Surf Shop in New Smyrna Beach, Florida, where customers flocked to buy boards in anticipation of the storm's high waves. Officials along the coast warned of rip currents, waves and high tides – all of which can be dangerous but also tend to attract adventurous surfers. The waters had already become dangerous in South Carolina, where rescuers were searching for a missing swimmer.

The coastguard said crews in Charleston harbour rescued three people and a dog from a sinking vessel on Sunday.